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This is one of our many quizzes on Linear equations. Click on this to access more such competitive quizzes on Algebra.

Linear equations Quiz 2

mathematics

 Express $23x - \dfrac{5}{7}y = 18$ in the general form

 The general form of a linear equation is $ax + by + c = 0$

 $  23x - \dfrac{5}{7}y = 18 \\  \dfrac{{161x - 5y}}{7} = 18 \\  161x - 5y = 126 \\   \Rightarrow 161x - 5y - 126 = 0 \\  $

 Find out the slope of the given equation – $8y + 19 = 7x$

 Convert the equation to slope intercept form, that is, $y = mx + c$ and then find the value of m.

  $  8y + 19 = 7x \\   \Rightarrow 8y = 7x - 19 \\   \Rightarrow y = \dfrac{7}{8}x - \dfrac{{19}}{8} \\  $

 A line passes through the points (2,9) and (9,13). Find the equation of this line in general form.

 The equation of line passing through the points $({x_1},{y_1})$ and $({x_2},{y_2})$ is given as –  $y - {y_1} = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}(x - {x_1})$

  $  y - 9 = \dfrac{{13 - 9}}{{9 - 2}}(x - 2) \\   \Rightarrow y - 9 = \dfrac{4}{7}(x - 2) \\   \Rightarrow 7y - 63 = 4x - 8 \\   \Rightarrow 4x - 7y + 55 = 0 \\  $

 Find the x and y intercept of the line $16x + 19y = 9$

 When the x and y intercepts of a line are a and b respectively then its equation is given as $\dfrac{x}{a} + \dfrac{y}{b} = 1$

  $  16x + 19y = 9 \\  \dfrac{{16x}}{9} + \dfrac{{19y}}{9} = 1 \\  \dfrac{x}{{\dfrac{9}{{16}}}} + \dfrac{y}{{\dfrac{9}{{19}}}} = 1 \\  $

 Find the equation of the line that is perpendicular to the line $y - 9x = 19$ and passes through $(3,7)$

 The product of the slope of two perpendicular lines is equal to -1. Equation of a line having slope m and passing through $({x_1},{y_1})$ is given as $y - {y_1} = m(x - {x_1})$

  $  y - 9x = 19 \\  y = 9x + 19 \\  $ So ${m_1} = 9$ $  {m_1}.{m_2} =  - 1 \\   \Rightarrow {m_2} = \dfrac{{ - 1}}{9} \\  $ Equation of required line is given as – $  y - 7 = \dfrac{{ - 1}}{9}(x - 3) \\  9y - 63 =  - x + 3 \\  x + 9y - 66 = 0 \\  $